Here is a table of proposed experiments for creating enormous superpositions of matter, along with two that have actually been performed (KDTL and MUSCLE, in green). Importantly, all of them describe superpositions whose spatial extent is comparable to or larger than the size of the object itself. Many are quite speculative. I’d like to keep this table updated, so send me references if you think they should be included. [Updated: 2026-Jan-23]
| experiment | ref. | object composition | object radius (nm) | nucleon count | superp. size (nm) | lifetime (ms) | repetition rate (Hz) |
|---|---|---|---|---|---|---|---|
| KDTL | [1-3] | Oligoporphyrina | ∼1 | 2.7 × 104 | 266 | 1.24 | 10,000 |
| OTIMA | [4-6] | Gold (Au) | 5 | 6 × 106 | 79 | 94 | 600 |
| Bateman et al. | [7] | Silicon (Si) | 5.5 | 1.1 × 106 | 150 | 140 | 0.5 |
| Geraci et al. | [8] | Silica (SiO2) | 6.5 | 1.6 × 106 | 250 | 250 | 0.5 |
| Wan et al. | [9] | Diamond (C) | 95 | 7.5 × 109 | 100 | 0.05 | 1 |
| MAQRO | [10-13] | Silica (SiO2) | 120 | 1 × 1010 | 100 | 100,000 | 0.01 |
| Pino et al. | [14] | Niobium (Nb) | 1,000 | 2.2 × 1013 | 290 | 450 | 0.1 |
| Stickler et al.b | [15-17] | Silicon (Si) | 5 | 5 × 105 | 20 | 20 | 5* |
| Delić et al. | [18] | Silica (SiO2) | 71 | 2 × 109 | 100 | 10 | 10* |
| Marshman et al. | [19] | Diamond (C) | 100 | 1 × 1010 | 20,000 | 1,000 | 0.1* |
| Wood et al. | [20] | Diamond (C) | 125 | 1.7 × 1010 | 250 | 100 | 1* |
| Xiang et al.c | [22] | Diamond (C) | 50 | 1 × 109 | 500 | 100 | 1* |
| MUSCLE | [21] | Sodium (Na) | 4 | 1.7 × 105 | 133 | 12.3 | 20 |
| MUSCLE-2d | [21] | Sodium (Na) | 7 | 1 × 106 | 133 | 80 | 1* |
The rows above the black line are an updated version of those appearing in Table 1 of my 2017 paper with Itay Yavin. The rows below the black line were released since then. Delić et al. was discussed by me here. Many of the repetition rates were either taken directly from the relevant proposal or were estimated based on private correspondence with the authors. However, the repetition rates marked with an asterisk (*) indicate that I just inverted the the superposition lifetime and introduced a factor of ten of overhead.
I emphasize that I have erred on the side of inclusivity; some of these proposals are very speculative, with big unsolved technical challenges and mushy parameters. Ask your local experimentalist which ones you should take seriously.
References
[1] S. Gerlich, S. Eibenberger, M. Tomandl, S. Nimmrichter, K. Hornberger, P. J. Fagan, J. Tüxen, M. Mayor, and M. Arndt, Nature communications 2, 263 (2011).[2] S. Eibenberger, S. Gerlich, M. Arndt, M. Mayor, and J. Tüxen, Physical Chemistry Chemical Physics 15, 14696 (2013).
[3] Y. Fein, P. Geyer, P. Zwick, F. Kiałka, S. Pedalino, M. Mayor, S. Gerlich, and M. Arndt, Nature Physics 15, 1242–1245 (2019).
[4] S. Nimmrichter, P. Haslinger, K. Hornberger, and M. Arndt, New Journal of Physics 13, 075002 (2011).
[5] S. Nimmrichter, K. Hornberger, P. Haslinger, and M. Arndt, Physical Review A 83, 043621 (2011).
[6] M. Arndt and K. Hornberger, Nature Physics 10, 271 (2014).
[7] J. Bateman, S. Nimmrichter, K. Hornberger, and H. Ulbricht, Nature Communications 5, 4788 (2014).
[8] A. Geraci and H. Goldman, Physical Review D 92, 062002 (2015).
[9] C. Wan, M. Scala, G. W. Morley, A. A. Rahman, H. Ulbricht, J. Bateman, P. F. Barker, S. Bose, and M. S. Kim, Physical Review Letters 117, 143003 (2016).
[10] R. Kaltenbaek, “Macroscopic quantum experiments in space using massive mechanical resonators (MQES) –
technical note #3,” Tech. Rep., Study conducted under contract with the European Space Agency (2012).
[11] R. Kaltenbaek et al. (MAQRO Collaboration), EPJ Quantum Technology 3, 5 (2016).
[12] R. Kaltenbaek, “Testing quantum physics in space using high-mass matter-wave interferometry,” Proceedings of 50th Rencontres de Moriond; Gravitation: 100 Years after GR, pp. 141 [arXiv:1508.07796] (2015).
[13] R. Kaltenbaek et al., “MAQRO — BPS 2023 Research Campaign Whitepaper” [arXiv:2202.01535] (2022)
[14] H. Pino, J. Prat-Camps, K. Sinha, B. P. Venkatesh, and O. Romero-Isart, Quantum Sci. Technol. 3, 25001 (2018).
[15] B. Stickler, B. Papendell, S. Kuhn, B. Schrinski, J. Millen, M. Arndt, and K. Hornberger, New J. Phys. 20, 122001 (2018).
[16] B. Stickler, K. Hornberger, and M. Kim, Nature Reviews Physics 3, 589–597 (2021).
[17] B. Schrinski, B. Stickler, and K. Hornberger, Phys. Rev. A 105, L021502 (2022).
[18] U. Delić, M. Reisenbauer, K. Dare, D. Grass, V. Vuletić, N. Kiesel, and M. Aspelmeyer, Science 367, 892-895 (2020).
[19] R. Marshman, A. Mazumdar, R. Folman, and S. Bose, “Large Splitting Massive Schrödinger Kittens” [arXiv:2105.01094] (2021).
[20] B. D. Wood, S. Bose, and G. W. Morley, Physical Review A 105, 012824 (2022).
[21] S. Pedalino, B. E. Ramírez-Galindo, R. Ferstl, K. Hornberger, M. Arndt, and S. Gerlich, Nature 649, 866–870 (2026).
[22] Y. Margalit, O. Dobkowski, Z. Zhou, O. Amit, Y. Japha, S. Moukouri, D. Rohrlich, A. Mazumdar, S. Bose, C. Henkel, and R. Folman, Science Advances 7, eabg2879 (2021).
[23] J. Wardak, T. Georgescu, G. Gasbarri, A. Belenchia, and H. Ulbricht, “Nanoparticle Interferometer by Throw and Catch” [arXiv:2312.12974] (2023); Atoms 12, 7 (2024).
Footnotes
(↵ returns to text)
- To achieve their highest masses, the KDTL interferometer has superposed molecules of functionalized oligoporphyrin, a family of organic molecules composed of C, H, F, N, S, and Zn with molecular weights ranging from ~19,000 Da to ~29,000 Da. (The units here are Daltons, also known as atomic mass units (amu), i.e., the number of protons and neutrons.) The distribution is peaked around 27,000 Da.↵
- The Stickler et al. experiment is a nanorod in an orientation superposition rather than a nanosphere in a position superposition, so I have estimated the effective parameters for the amount of mass superposed in space.↵
- Xiang et al. describe range of possible masses, with the higher end not be superposed over the object size. We pick an intermediate mass (109 amu) and identify other parameters through interpolation.↵
- This refers to the proposed modification of MUSCLE to use 1 MDa nanoparticles traveling at 25 m/s, as discussed by Pedalino et al..↵
